The Italians currently stand second in Group H heading into the final pool game.
The Rossoneri lie one-point clear of third-place Ajax and are two adrift of already-qualified Barcelona, who host Celtic in the other group match.
AC Milan midfielder Kaka knows his team is in for a testing time as only a victory will serve Ajax to join Barca in the next round.
Kaka said: "This is a crucial game for the two sides and it's going to be a battle.
"We don't want to let our fans down and we will do all that we can to progress to the next round."
The Italians have lost just once in the Champions League this season - a 3-1 defeat at Barcelona - but have been less convincing in Serie A.
Massimiliano Allegri's men go into the encounter on the back of Saturday's 2-2 draw at Livorno that saw them drop to ninth in the standings.
Milan have won just one of their last eight league games and trail 14 points behind Napoli, who hold the last Champions League qualifying spot.
"We will need to show a vast improvement against Ajax from our performance at Livorno," Allegri said.
Kaka will have plenty of motivation to score on Wednesday as he is one strike shy of a century of goals with the Rossoneri colours.
Kaka is set to play in support of attacking pair Mario Balotelli and Stephan El Shaarawy.
"It would be fantastic to score my 100th goal at the San Siro against Ajax," he said.
Last month's 2-1 triumph over Barcelona - that followed their 1-0 victory over Celtic - allowed Ajax to go into the final pool game with all to play for.
"We want to return to play in the Champions League after the Christmas break," Ajax coach Frank De Boer said. "I think we have the qualities to do that.
"But we'll need to play against Milan the same way as we did against Barcelona."
Ajax have reason to be confident for they won 2-0 at AC Milan back in the 2010-11 Champions League campaign in what was De Boer's first game in charge.
The Dutch giants have already assured themselves Europa League football next year as bottom-side Celtic are four points behind them and unable to catch them.
Ajax warmed up for the match with Saturday's 4-0 triumph over NAC Breda.
The outcome allowed the Godenzonen to move two point adrift of Eredivisie leaders Vitesse.
Ajax are without the services of injured trio Nicolai Boilesen, Siem De Jong and Lerin Duarte, while defender Joel Veltman must serve a one-match ban.
The good news for De Boer is that striker Kolbeinn Sigthorsson has recovered from an ankle injury.
The hosts will be without midfielder Valter Birsa, who is sidelined with a thigh injury.